When Hiroto is writing, there is $0.92$ probability that there will be no spelling mistakes on a page. One day, Hiroto writes an essay that is $11$ pages long. Assuming that Hiroto is equally likely to have a spelling mistake on each of the $11$ pages, what is the probability that he will have a spelling mistake on at least one of the pages? Round your answer to the nearest tenth. $P(\text{at least one mistake})=$
Strategy In this situation it is much easier to calculate the probability of the event we are looking for (he makes at least one mistake) by calculating the probability of its complement (he makes no spelling mistakes), and subtracting from $1$. In other words, we can use this strategy: $P(\text{at least one mistake})=1-P(\text{no mistakes on all }11)$ Calculations $\begin{aligned} &\phantom{=}P(\text{at least one mistake}) \\\\ &=1-P(\text{no mistakes on all }11) \\ \\ &=1-(0.92)^{11} \\ \\ &\approx 1-0.3996 \\ \\ &\approx 0.6004\end{aligned}$ Answer $P(\text{at least one mistake}) \approx 0.6$